Question

Prove that the bisectors drawn from the vertex of the base of an equilateral triangle are equal

Answer 1

Let AD be the bisector of ∠A.

To prove:- BD=DC

Proof:-

In △ABD&△ACD

AB=AC(∵△ABC is an isosceles triangle)

∠BAD=∠CAD(∵AD is the bisector of ∠A)

AD=AD(Common)

By S.A.S.-

△ABD≅△ACD

By corresponding parts of congruent triangles-

⇒BD=DC

Hence proved that the perpendicular drawn from the vertex angle to the base bisect the vertex angle and base.